Eigenlogic: Interpretable Quantum Observables with applications to Fuzzy Behavior of Vehicular Robots

Zeno Toffano (1) , François Dubois (2)

1 L2S - Laboratoire des signaux et systèmes
2 LM-Orsay - Laboratoire de Mathématiques d'Orsay

This work proposes a formulation of propositional logic, named Eigenlogic, using quantum observables as propositions. The eigenvalues of these operators are the truth-values and the associated eigenvectors the interpretations of the propositional system. Fuzzy logic arises naturally when considering vectors outside the eigensystem, the fuzzy membership function is obtained by the Born rule of the logical observable. This approach is then applied in the context of quantum robots using simple behavioral agents represented by Braitenberg vehicles. Processing with non-classical logic such as multivalued logic, fuzzy logic and the quantum Eigenlogic permits to enlarge the behavior possibilities and the associated decisions of these simple agents.

Keywords: quantum agents; multivalued logic; fuzzy logic; robots; Braitenberg vehicles

Domains: Physics [physics]; Quantum Physics [quant-ph]; Humanities and Social Sciences; Library and information sciences

Zeno Toffano, François Dubois. Eigenlogic: Interpretable Quantum Observables with applications to Fuzzy Behavior of Vehicular Robots. WOSC 17th Congress 2017: Science with and for Society: Contributions of Cybernetics and Systems, World Organisation of Systems and Cybernetics, Jan 2017, Rome, Italy. ⟨hal-01562148⟩